Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896879 | Journal of Number Theory | 2018 | 18 Pages |
Abstract
In this article, we study the Q-rational torsion subgroups of the Jacobian varieties of modular curves. The main result is that, for any positive integer N, J0(N)(Q)tor[qâ]=0 if q is a prime not dividing 6â
Nâ
âp|N(p2â1). To prove the result, we explicitly construct a collection of Eisenstein series with rational Fourier expansions, and then determine their constant terms to control the size of the rational torsion subgroups.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yuan Ren,